Plot hole: As Josh arrives at the security gate of the White House, protestors are gathered, chanting and otherwise talking loudly. He enters the gate, makes his way to the north entrance of the West Wing, and as he enters the lobby, the crowd is still heard quite plainly, just as loudly as at the gate, as if they were right outside the door, yet the protestors are much too far away to be heard so loudly, if at all.
Plot hole: The Zoey Bartlett kidnap crisis cliffhanger that stretches across the end of Season 4 and the beginning of Season 5 makes no sense in terms of time. Charlie pulls out a note from his wallet that says they will dig up a bottle of champagne on May 7 - Zoey's graduation night. They do. Later that night she is abducted. She is gone three days. Four days later (in "Jefferson Lives") Abby chews out Leo, saying, "It's only been four days and her bruises have not yet begun to heal." The date should be May 14th. However, "Jefferson Lives" supposedly occurs on the Fourth of July - Zoey says it's the Fourth and they all watch the Capitol Fireworks at the end. Boy, that sure was a short month of June.